Towards a hypergraph version of the Pósa-Seymour conjecture

Abstract

We prove that for fixed $r\ge k\ge 2$, every $k$-uniform hypergraph on $n$ vertices having minimum codegree at least $(1-(\left(\genfrac{}{}{0ex}{}{r-1}{k-1}\right)+\left(\genfrac{}{}{0ex}{}{r-2}{k-2}\right){)}^{-1})n+o(n)$ contains the $(r-k+1)$th power of a tight Hamilton cycle. This result may be seen as a step towards a hypergraph version of the Pósa-Seymour conjecture. Moreover, we prove that the same bound on the codegree suffices for finding a copy of every spanning hypergraph of tree-width less than $r$ which admits a tree decomposition where every vertex is in a bounded number of bags.

References in corpus (1)

• Squares of Hamiltonian cycles in 3-uniform hypergraphs

Cited by in corpus (1)

• Counting spanning subgraphs in dense hypergraphs